The present invention relates to the assessment of corrosion, and more particularly, to a system and method for predicting the degree to which a tube array has degraded over a period of time due to corrosion in a particular operating environment.
Arrays of tubes can be found in a variety of industrial and process plants, where multiple sources, or mechanisms, of corrosion can attack the tubes, leading to deterioration and perforation. This problem is of particular concern in nuclear power plants, where nuclear steam generators, each containing upwards of a thousand tubes, can be subject to concurrent corrosion attacks on both primary (inner) and secondary (outer) tube surfaces. More so than in other industrial or process contexts, tube deterioration or failure in a nuclear steam generator, poses safety risks, in addition to performance (e.g., heat transfer) degradation. Moreover, excessive leakage resulting from failed tubes in the steam generator, can require the unscheduled shut-down of the power plant.
For these and other reasons, operators of power plants which employ nuclear steam generators, inspect and plug or repair tubes as necessary during cycle outages, to minimize total leakage during the next operating cycle. The prediction of which particular tubes in the array will be the next to fail, is virtually impossible. Because every tube cannot be inspected at every plant outage, yet the operator must be reasonably confident that the number of failures expected to occur during the next operating cycle will not result in the premature shut-down of the plant, efforts have been made to model, and therefore predict, the gross failure rates of tubes in the steam generator.
The failure rates of tubes in steam generators are typically computed using the so-called Weibull failure model, which takes the general form: EQU P.sub.N (t)=1-exp(-(t/a).sup.b) [1]
where:
P.sub.N (t)=proportion failed at time (t) (failure mode N) PA1 b=shape parameter of Weibull distribution PA1 a=scale parameter of Weibull distribution
The total numbers of tubes requiring repair from N separate causes is obtained by Boolian summation involving risks associated with each failure mode. This process has proven adequate for cases in which the parameters b,a of each Weibull distribution are well known. The major deficiency in the existing methodology is the lack of a fully probabilistic method for dealing with large uncertainties in the values of the two Weibull parameters, and the subsequent inability to obtain quantifiable confidence estimates of the minimum and maximum tube repair requirements.